What to see and do in London for a week?

I'll be going to London for a week in mid-September and so far I don't have much of a plan.I don't really know what's worth seeing or what I would like and I'd appreciate some help deciding on what to do.

I know a few must sights like

London Tower

Tower Bridge

Big Ben

Windsor Palace

Buckingham Palace

London Eye

Piccadilly Circus

Madame Tussauds

Westminster Abbey

St. Paul's Cathedral

but that's about it.Any tips for other must-see sights or great activities?

And maybe even some more recommendations for me in particular?I mostly like

architecture

historical sites

parks, etc.

(non- contemporary) art

museum (there are so many, I don't know which are good or not, I mostly prefer those which visually appealing exhibitions)

But I'm also open for other things that are interesting or fun

PS: Is there a site where you can schedule sightseeing or something like it? I want to avoid trying to visit sites on opposite ends of town

I think you've pretty much answered your own question. However you might also like to:

- wander the streets around Notting Hill- go to Camden markets (best on weekends, but gets extremely busy)- Hyde Park, Green Park, Kensington Gardens- Richmond for the day (about 20 mins out of town)- Brighton for the day (an hour by train from London Victoria)- Harrods- Pubs, pubs and more pubs

Second all of James's recommendations. Also maybe look at Greenwich, which is a nice afternoon out by boat from the centre of town, national maritime museum, greenwich observatory and cutty sark are there.